Question

Distance of chord AB from the centre of a circle is 8 cm. Length of the chord AB is 12 cm. Find the diameter of the circle.

Answer 1

Let point O be the center of the circle.

seg OC ⊥ chord AB such that, A-C-B

AC = `1/2` AB          ...(The perpendicular drawn from the center of the circle to the chord bisects the chord.)

∴ AC = `1/2 xx 12`

∴ AC = 6 cm

Draw line OA.

In ∆OCA, From Pythagoras theorem,

OA² = OC² + AC²

∴ OA² = 8² + 6²

∴ OA² = 64 + 36

∴ OA² = 100

∴ OA = `sqrt(100)`

∴ OA = 10 cm

∴ Diameter of circle = `2 xx10`

∴ Diameter of circle = 20 cm